how can i find the sum of three consecutive numbers

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- amina_soneviseth

how can i find the sum of three consecutive numbers

- katieb

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- mathstudent55

You mean they are unknown, and you need to write an equation?

- SolomonZelman

If the lowest integer is x, then the second one is (x+1) and the third one is (x+2).
The sum would be = `x + (x+1) + (x+2)` = x + x + x + 1 + 2 = `3x+3`

- amina_soneviseth

sorry i meant the sum of three consecutive even integers of -54 how do i find the answer?

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## More answers

- mathstudent55

Since they are even, then the difference between them is 2.
Use the idea that @SolomonZelman gave you, but modify it this way:
Let the smallest number be x.
Then the next larger number is x + 2
The largest of the three numbers is x + 4.
The sum then is:
x + x + 2 + x + 4
Set that sum equal to -54.
Then solve for x.
That gives you the smallest number. Then add 2 to x to find the middle number, and add 4 to x to find the largest number.

- amina_soneviseth

i dont understand, why x? and how do i get to the answer thank you

- freckles

Let's say you have the number 2.
And I ask you what is the next even number after 2, you would say 2+2 or 4 right?
And if I asked for the third even number after 2, you would say 2+4 or 6 right?
Let's say you have the number x. (assume x is even)
The next even number after x, would be x+2.
The third even number after x, would be x+4.
The sum of these numbers would be (x)+(x+2)+(x+4)
or dropping the ( ) you could say x+x+2+x+4
and you want this to be equal to -54 as you said above...
So you have the equation x+x+2+x+4=-54 to solve.
So you will need to first combine your like terms on the left hand side.
That is do you know what x+x+x=? and you should know 2+4=6...

- amina_soneviseth

so its x+x+x+2+4= -54? where do i go from there? :D

- IrishBoy123

on the left- hand side of your equation:
A/ add up the x's
B/ add up the numbers

- IrishBoy123

IOW, simplify it a bit... :p

- mathstudent55

In math (Algebra) we use letters (called variables) to represent unknown amounts.
Since we don't know what the three even numbers are, we use the letter x, here called a variable, to represent the smallest of the three unknown even numbers.
Once we choose x to represent the smallest of three even numbers, the other two even numbers are x + 2 and x + 4, as explained in an earlier response above.
The sum of the three numbers is -54, so we can write this as an equation:
x + x + 2 + x + 4 = -54
We now combine all x's on the left side.
x is the same as 1x
1x + 1x + 2 + 1x + 4 = -54
1x + 1x + 1x + 2 + 4 = -54
Adding 1x + 1x + 1x, we get 3x;
also, 2 + 4 = 6, so we now have
3x + 6 = -54
Now we need to subtract 6 from both sides of the equation.
3x + 6 = -54
- 6 -6
--------------
3x = -60
Now we divide both sides by 3 to get:
3x/3 = -60/3
x = -20
Since x represents the smallest of the three numbers,
now we know that the smallest of the 3 consecutive even numbers is -20.
The next number is x + 2 = -20 + 2 = -18
The largest of the 3 number is x + 4 = -20 + 4 = -16
The numbers are -20, -18, -16
Now let's check.
-20, -18, and -16 are consecutive even numbers.
What is -20 + (-18) + (-16) = ?
-20 + (-18) + (-16) = -54
The sum of the three numbers is -54, so our answer is correct.
The three numbers are -20, -18, and -16.

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